3. If dy = x^2y^2 , then what is d2y/dx2

[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\boxed{A}\qquad \sqrt[4]{8}\implies \sqrt[4]{2^3}\implies 2^{\frac{3}{4}} \\\\\\ \boxed{B}\qquad \sqrt[4]{2^3}\implies 2^{\frac{3}{4}} \\\\\\ \boxed{C}\qquad 2^{\frac{1}{4}}\times 2^{\frac{1}{2}}\implies 2^{\frac{1}{4}+\frac{1}{2}}\implies 2^{\frac{1+2}{4}}\implies 2^{\frac{3}{4}} \\\\\\ \boxed{D}\qquad \left( 2^{\frac{1}{4}} \right)^{\frac{1}{2}}\implies 2^{\frac{1}{4}\cdot \frac{1}{2}}\implies 2^{\frac{1}{8}}\qquad \textit{\large \checkmark}[/tex]

The length of the shorter string is 18 inch while that of the longer string is 30 inch.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let s represent the length of the shorter string.

One piece is 12 inches longer than the other

Length of longer string = s + 12

Since a 48-inch piece of string is cut into two pieces. Hence:

s + (s + 12) = 48

2s + 12 = 48

2s = 36

s = 18

Length of longer string = 18 + 12 = 30

The length of the shorter string is 18 inch while that of the longer string is 30 inch.

Find out more on equation at: https://brainly.com/question/2972832

708 ml

When each box contains 236 ml of juice and she pours three boxes into the bowl, you need to multiply 236 by 3. After completing the calculation, you would get 708.

Answer:

check online for more information

Answer:

Step-by-step explanation:

∠L and ∠N are identical

3x + 40 = 5x

       40 = 2x

        20 = x

So ∠L and ∠N are both 100°

Internal angles on a quadrilateral sum to 360° and ∠M and ∠O are identical

∠M = (360 - 2(100))/2 = 80°

Answer:

Step-by-step explanation:

Not near enough information to know.

I ASSUME that the pool is surrounded by a walkway of constant width (w = 2 ft, from comments)

The pool shape is important as well. No mention of  the shape

If the pool is circular and the walkway is 3 ft wide

the fence encloses a diameter of 110/π = 35 ft

so the diameter of the pool would be 35 - 2(3) = 29 ft.

POOL IS RECTANGULAR from comments

If the pool is square and the walkway is 2 ft wide, each side of the fence is

110 / 4 = 27.5 ft and the pool would be 27.5 - 2(2) = 23.5 ft on a side.

There are an infinite number of rectangular width and length dimensions and walkway dimensions which would result in a fence length of 110 ft.

Edit from comments

Still an infinite number of rectangular length an width dimensions for a pool with a 2 ft wide walkway around it.

Let's say that we are told the pool is 12 ft wide with 2 ft walkway.

Let L be the pool length

110 = 2(12 + 2(2)) + 2(L + 2(2))

110 = 32 + 2L + 8

70 = 2L

L = 35 ft

Answer:

A

Step-by-step explanation:

The square root of 50 is less than the square root of 78.

Answer:

so 6x = -6y + 5

divide by 6

x = 5

Step-by-step explanation:

Answer:

[tex]-a-\frac{a^2}{2}-\frac{a^3}{3}-\frac{a^4}{4}-...-\frac{a^n}{n}-...[/tex]

Step-by-step explanation:

1) the rule is:

[tex]ln(1+a)=a-\frac{a^2}{2}+\frac{a^3}{3}-\frac{a^4}{4}+...+(-1)^{n-1}\frac{a^n}{n}+...[/tex]

2) according to the rule above:

[tex]ln(1+(-a))=(-a)-\frac{(-a)^2}{2}+\frac{(-a)^3}{3}-\frac{(-a)^4}{4}+...+(-1)^{n-1}\frac{(-a)^n}{n}+...[/tex]

finally,

[tex]ln(1-a)=-a-\frac{a^2}{2}-\frac{a^3}{3}-\frac{a^4}{4}-...-\frac{a^n}{n}-...[/tex]

Answer:

zero point zero three six

Step-by-step explanation:

of course, we have to use Pythagoras.

c² = a² + b²

c is the Hypotenuse = the side opposite of the 90° angle.

and here is the problem : are 9 and 12 the legs. or is one of them the Hypotenuse ?

I don't know from the description.

let's see what we get one way or the other :

assumption : the known sides are the "legs".

c² = 9² + 12² = 81 + 144 = 225

c = 15 ft

that is a nice number. so, it looks like that was the intention.

just to be sure, here also the other options :

9² = 12² + side²

81 = 144 + side² that makes side² negative, so, not valid.

12² = 9² + side²

144 = 81 + side²

63 = side²

side = sqrt(63) this is not a nice round number, so, we go with the first option.

therefore, the 3 sides are

9 ft, 12 ft, 15 ft

perimeter = 9+12+15 = 36 ft

area = baseline×height/2

since this is a right-angled triangle, the "legs" with the enclosed 90° angle serve as baseline and height.

area = 9×12/2 = 9×6 = 54 ft²

Step-by-step explanation:

A= C. - By

x. ×

answer by a

huhuhu

Answer:

I think the answer is C.....

Answer:

maybe it's 12 but i don't know...

Answer: 301.44 cubic inches.

Step-by-step explanation:

The formula for the volume of a cone is [tex]V = \pi r^2 \frac{h}{3}[/tex], so by plugging in the radius (6) and height (8), and using 3.14 as pi, you can get 301.44 as the total volume.

Since it is volume, it is in inches cubed, Therefore, the final answer is 301.44 cubic inches.

I hope this helps! :)

Answer:

B.)The points in the scatterplot follow a line, so a linear model would fit the data better

A.)The model is not a good fit because there is a pattern in the residual plot.

Step-by-step explanation:

The linear model would best fit the scatter plot while the quadratic model would fit the residual plot. The true statements are: B and C.

A linear model is appropriate for data points that lie along a straight line on graph. If the line is not straight but curved and changes direction, a quadratic model is a better model for such data.

Thus, since the data points on the scatter plot are on a straight line, a linear model would fit the data.

For the residual plot that changes direction, a quadratic model would better fit the data.

The true statements are therefore: B and C.

Learn more about linear and quadratic model on:

https://brainly.com/question/13496810

#SPJ2

Answer:

y = 2x-7

Step-by-step explanation:

I'm not really sure this is the slope-intercept form, as I've never called it like that before, but if it is, there you go.

Answer:

[tex]\huge\boxed{\sf y = 2x - 7}[/tex]

Step-by-step explanation:

Given equation is:

2x - y = 7

Add y to both sides

2x = 7 + y

Invert the equation

7 + y = 2x

Subtract 7 to both sides

y = 2x - 7

This is the required equation in slope-intercept form y = mx + b where m is slope and b is y-intercept.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

yes i love this app , this app so good

Answer:

24

Step-by-step explanation:

By BODMAS rule,

[ ( 15 + 1 ) / 2 - 4 ] * 6

= [ 16 / 2 - 4 ] * 6

= [ 8 - 4 ] * 6

= 4 * 6

= 24

Based on the information given, the value of the equation will be -48.

From the information given, the expression is given as:

= (15+1)/2-4]*6

We'll solve the bracket first.

= (15+1)/2-4]*6

= (16 / 2 - 4) × 6

= (16/-2) × 6

= -8 × 6

= -48

In conclusion, the value of the equation will be -48.

Learn more about equations on:

https://brainly.com/question/13802812

Answer:

C) Discrete made up of individual points

The option that best suits him is 4.0% Interest Rate for 30 years with a monthly payment of $ 1,193.54 with $ 10,362 in Closing Costs.

Given that Mr. Schnee is refinancing his home, and his loan officer has presented him with two offers, to determine which offer should he take in order to maximize his benefit, the following calculation must be performed:

A) 4.5% Interest Rate for 30 years with a monthly payment of $ 1,266.71 with $ 256 Closing Costs

1,266.71 x 30 x 12 + 256 = X

1,266.71 x 360 + 256 = X

456,015.60 + 256 = X

456,271.60 = X

B)4.0% Interest Rate for 30 years with a monthly payment of $ 1,193.54 with $ 10,362 in Closing Costs

1,193.54 x 30 x 12 + 10,362 = X

1,193.54 x 360 + 10,362 = X

429,674.40 + 10,362 = X

440,036.40 = X

Therefore, the option that best suits him is 4.0% Interest Rate for 30 years with a monthly payment of $ 1,193.54 with $ 10,362 in Closing Costs.

Learn more about maths in https://brainly.com/question/25866144

Divergence:

div(F) = ∂(3x²y² + 2z)/∂x + ∂(3x² + y + yz)/∂y - ∂(3x²z² + 2yx + xyz)/∂z

div(F) = 6xy² + 1 + z - 6x²z - xy

Curl:

curl(F) = [∂(3x² + y + yz)/∂z + ∂(3x²z² + 2yx + xyz)/∂y] i

… … … … … - [∂(3x²y² + 2z)/∂z + ∂(3x²z² + 2yx + xyz)/∂x] j

… … … … … + [∂(3x²y² + 2z)/∂y - ∂(3x² + y + yz)/∂x] k

curl(F) = (-xz - 2x - y) i + (6xz² + yz + 2y + 2) j + (6x - 6x²y) k

Step-by-step explanation:

to make the equation true the value of y must be.

hope it helps.

stay safe healthy and happy.

Answer:

y=-/+9

Step-by-step explanation:

y^2=81

find the square root

y=positive/negative 9

Answer:

99th term is 51

Step-by-step explanation:

Arithmetic sequence equation

a1= first term = 2

d= common difference = 0.5 or 1/2

2, 5/2 = 5/2 - 2 = 0.5 or 1/2

3 - 5/2 = 1/2

7/2 - 3 = 1/2

an = a1 + (n - 1)d

a99 = 2 + (99-1) 1/2

a99= 2 + 98 (1/2)

a99 = 2 + 49

a99 = 51

The compound interest is applied to the remaining balance in the account

each subsequent year.

Reasons:

The given compound interest rate, r = 6.25% = 0.0625

The balance in the account after 2 years, A = $700

Required:

The required deposit, P, that gives the given account balance after 2 years.

Solution:

The following is the compound interest formula to use;

Where;

t = 2 years

We get;

[tex]\displaystyle P = \mathbf{ \frac{A}{(1 + r)^t}}[/tex]

Which gives;

[tex]\displaystyle P = \frac{700}{(1 + 0.0625)^2} \approx \mathbf{620.07}[/tex]

Learn more about compound interest here:

https://brainly.com/question/10028292

Answer:

-0.2

Step-by-step explanation:

pls give me brainliest if possible

Answer:

3;87

Step-by-step explanation:

Since they are complementary, they add up to 90°. This allows you to write the equation

[tex]x+(16x+39) = 90 \rightarrow 17x=90-39 \rightarrow 17x=51 x=\frac{51}{17}=3[/tex]

The second angle measures then [tex]90-3 = 87[/tex]